Long-running applications are often subject to failures. Once failures occur, it will lead to unacceptable system overheads. The checkpoint technology is used to reduce the losses in the event of a failure. For the two-level checkpoint recovery scheme used in the long-running tasks, it is unavoidable for the system to periodically transfer huge memory context to a remote stable storage. Therefore, the overheads of setting checkpoints and the re-computing time become a critical issue which directly impacts the system total overheads. Motivated by these concerns, this paper presents a new model by introducing i-checkpoints into the existing two-level checkpoint recovery scheme to deal with the more probable failures with the smaller cost and the faster speed. The proposed scheme is independent of the specific failure distribution type and can be applied to different failure distribution types. We respectively make analyses between the two-level incremental and two-level checkpoint recovery schemes with the Weibull distribution and exponential distribution, both of which fit with the actual failure distribution best. The comparison results show that the total overheads of setting checkpoints, the total re-computing time and the system total overheads in the two-level incremental checkpoint recovery scheme are all significantly smaller than those in the two-level checkpoint recovery scheme. At last, limitations of our study are discussed, and at the same time, open questions and possible future work are given.